# Mass Number Of Carbon

Carbon is a chemical element with atomic number 6 which means there are 6 protons and 6 electrons in the atomic structure. The chemical symbol for Carbon is C. Atomic Mass of Carbon Atomic mass of Carbon is 12.0107 u.

## Atomic Number and Mass Number

When you study the periodic table, the first thing that you may notice is the number that lies above the symbol. This number is known as the atomic number, which identifies the number of protons in the nucleus of ALL atoms in a given element. The symbol for the atomic number is designated with the letter Z. For example, the atomic number (z) for sodium (Na) is 11. That means that all sodium atoms have 11 protons. If you change the atomic number to 12, you are no longer dealing with sodium atoms, but magnesium atoms. Hence, the atomic number defines the element in question.

### Mass Number Of Carbon 13

Recall that the nuclei of most atoms contain neutrons as well as protons. Unlike protons, the number of neutrons is not absolutely fixed for most elements. Atoms that have the same number of protons, and hence the same atomic number, but different numbers of neutrons are called isotopes. All isotopes of an element have the same number of protons and electrons, which means they exhibit the same chemistry. Because different isotopes of the same element haves different number of neutrons, each of these isotopes will have a different mass number(A), which is the sum of the number of protons and the number of neutrons in the nucleus of an atom.

Mass numbers of typical isotopes of Carbon are 12; 13. The total number of neutrons in the nucleus of an atom is called the neutron number of the atom and is given the symbol N. Neutron number plus atomic number equals atomic mass number: N+Z=A. The vast majority of all carbon found on Earth is 12 C. Almost 99% of all carbon on Earth is of this form. While only approximately 1% of all carbon on Earth is of the 13 C isotopic form, 14 C is still much rarer. Only one out of every trillion carbon atoms is 14 C. There are more carbon compounds than there are compounds of all other elements combined. It is found in abundance in the sun, stars, comets, and the atmospheres of most planets. Carbon-14, a radioactive isotope of carbon, is used to find the age of dead things by using radiocarbon dating.

Mass Number(A) = Number of Protons + Number of Neutrons

The element carbon (C) has an atomic number of 6, which means that all neutral carbon atoms contain 6 protons and 6 electrons. In a typical sample of carbon-containing material, 98.89% of the carbon atoms also contain 6 neutrons, so each has a mass number of 12. An isotope of any element can be uniquely represented as AZX, where X is the atomic symbol of the element, A is the mass number and Z is the atomic number. The isotope of carbon that has 6 neutrons is therefore 126C. The subscript indicating the atomic number is actually redundant because the atomic symbol already uniquely specifies Z. Consequently, it is more often written as 12C, which is read as “carbon-12.” Nevertheless, the value of Z is commonly included in the notation for nuclear reactions because these reactions involve changes in Z.

Figure 2.12: Formalism used for identifying specific nuclide (any particular kind of nucleus)

### Atomic Mass Unit

The atomic mass unit (u or amu) is a relative unit based on a carbon-12 atom with six protons and six neutrons, which is assigned an exact value of 12 amu's (u's). This is the standard unit for atomic or molecular mass, and 1 amu is thus 1/12th the mass of a 12C atom. This is obviously very small

1 amu = 1.66054x10-27Kg = 1.66054x10-24​​​​g

As a result of this standard, the mass of all other elements on the periodic table are determined relative to carbon-12. For example, a Nitrogen-14 atom with 7 protons and 7 neutrons has been experimentally determined to have a mass that is 1.1672 times that of carbon-12. So, the mass of the Nitrogen-14 atom must be 14.00643 u's. As you may have imagined, if another element has been chosen as the standard, the masses of the elements would have been completely different!

### Isotopic Distributions

Although carbon-12 is the most abundant type of isotope in carbon, it is not the only isotope. In addition to 12C, a typical sample of carbon contains 1.11% 13C, with 7 neutrons and 6 protons, and a trace 14C, with 8 neutrons and 6 protons. The nucleus of 14C is not stable, however, but undergoes a slow radioactive decay that is the basis of the carbon-14 dating technique used in archeology. Many elements other than carbon have more than one stable isotope; tin, for example, has 10 isotopes. The properties of some common isotopes are in Table 2.1.3. (Note: we will discuss the derivation of the atomic mass in the next section).

Table 2.1.3: Properties of Selected Isotopes

ElementSymbolAtomic Mass (amu)Isotope Mass NumberIsotope Masses (amu)Percent Abundances (%)
hydrogenH1.007911.00782599.9855
22.0141020.0115
boronB10.811010.01293719.91
1111.00930580.09
carbonC12.0111212 (defined)99.89
1313.0033551.11
oxygenO15.99941615.99491599.757
1716.9991320.0378
1817.9991610.205
ironFe55.8455453.9396115.82
5655.93493891.66
5756.9353942.19
5857.9332760.33
uraniumU238.03234234.0409520.0054
235235.0439300.7204
238238.05078899.274

Sources of isotope data: G. Audi et al., Nuclear Physics A 729 (2003): 337–676; J. C. Kotz and K. F. Purcell, Chemistry and Chemical Reactivity, 2nd ed., 1991.

Example 2.2.1

An element with three stable isotopes has 82 protons. The separate isotopes contain 124, 125, and 126 neutrons. Identify the element and write symbols for the isotopes.

Given: number of protons and neutrons

Asked for: element and atomic symbol

### Mass Number Of Carbon

Strategy:

1. Refer to the periodic table and use the number of protons to identify the element.
2. Calculate the mass number of each isotope by adding together the numbers of protons and neutrons.
3. Give the symbol of each isotope with the mass number as the superscript and the number of protons as the subscript, both written to the left of the symbol of the element.

Solution:

A The element with 82 protons (atomic number of 82) is lead: Pb.

B For the first isotope, A = 82 protons + 124 neutrons = 206. Similarly, A = 82 + 125 = 207 and A = 82 + 126 = 208 for the second and third isotopes, respectively. The symbols for these isotopes are 20682Pb, 20782Pb, and 20882Pb, which also can also be symbolized as Pb-206, Pb-207, and Pb-208.

Exercise (PageIndex{1})

What is the mass number of a phosphorous atom with 16 neutrons

31

Exercise (PageIndex{2})

How many protons, neutrons, and electrons are in As-74 atom?

### Mass Number Of Carbon 14

33 protons, 41 neutrons, 33 electrons

Exercise (PageIndex{3})

The actual mass of As-74 is 73.924 amu's.

A) What is the mass of As-74 in grams?

B) What is the mass of the arsenic atom relative to the carbon-12 atom?

A) Mass of As-74 = (73.924 amu) x (1.66054 x 10-24 g/amu) = 1.2275 x 10-22 g

B) Mass of As-74/Mass of C-12 = 73.924 amu/12 amu= 6.1603 ... so, the mass of an As-74 atom is about six times more than a C-12 atom.

#### Contributors

• Anonymous
• Modified by Joshua Halpern, Scott Sinex and Scott Johnson
• Bob Belford (UALR) and November Palmer (UALR)
• Ronia Kattoum(UALR)
Carbon-12, 12C
General
Symbol12C
Namescarbon-12, C-12
Protons6
Neutrons6
Nuclide data
Natural abundance98.93%
Parent isotopes12N
12B
Isotope mass12 u
Spin0
Excess energy0± 0 keV
Binding energy92161.753± 0.014 keV
Isotopes of carbon
Complete table of nuclides

Carbon-12 (12C) is the more abundant of the two stableisotopes of carbon (carbon-13 being the other), amounting to 98.93% of the elementcarbon;[1] its abundance is due to the triple-alpha process by which it is created in stars. Carbon-12 is of particular importance in its use as the standard from which atomic masses of all nuclides are measured, thus, its atomic mass is exactly 12 daltons by definition. Carbon-12 is composed of 6 protons, 6 neutrons, and 6 electrons.

## History

Before 1959, both the IUPAP and IUPAC used oxygen to define the mole; the chemists defining the mole as the number of atoms of oxygen which had mass 16 g, the physicists using a similar definition but with the oxygen-16 isotope only. The two organizations agreed in 1959/60 to define the mole as follows.

The mole is the amount of substance of a system which contains as many elementary entities as there are atoms in 12 gram of carbon 12; its symbol is 'mol'.

This was adopted by the CIPM (International Committee for Weights and Measures) in 1967, and in 1971, it was adopted by the 14th CGPM (General Conference on Weights and Measures).

In 1961, the isotope carbon-12 was selected to replace oxygen as the standard relative to which the atomic weights of all the other elements are measured.[2]

In 1980, the CIPM clarified the above definition, defining that the carbon-12 atoms are unbound and in their ground state.

In 2018, IUPAC specified the mole as exactly 6.022 140 76 × 1023 'elementary entities'. The number of moles in 12 grams of carbon-12 became a matter of experimental determination.

## Hoyle state

The Hoyle state is an excited, spinless, resonant state of carbon-12. It is produced via the triple-alpha process, and was predicted to exist by Fred Hoyle in 1954.[3] The existence of the 7.7 MeV resonance Hoyle state is essential for the nucleosynthesis of carbon in helium-burning red giant stars, and predicts an amount of carbon production in a stellar environment which matches observations. The existence of the Hoyle state has been confirmed experimentally, but its precise properties are still being investigated.[4]

The Hoyle state is populated when a helium-4 nucleus fuses with a beryllium-8 nucleus in a high-temperature (108K) environment with densely concentrated (105 g/cm3) helium. This process must occur within 10−16 seconds as a consequence of the short half-life of 8Be. The Hoyle state also is a short-lived resonance with a half-life of 2.4×10−16 seconds; it primarily decays back into its three constituent alpha particles, though 0.0413(11)% of decays occur by internal conversion into the ground state of 12C.[5]

In 2011, an ab initio calculation of the low-lying states of carbon-12 found (in addition to the ground and excited spin-2 state) a resonance with all of the properties of the Hoyle state.[6][7][8]

## Isotopic purification

The isotopes of carbon can be separated in the form of carbon dioxide gas by cascaded chemical exchange reactions with amine carbamate.[9]

## References

1. ^'Table of Isotopic Masses and Natural Abundances'(PDF). 1999.
2. ^'Atomic Weights and the International Committee — A Historical Review'. 2004-01-26.
3. ^Hoyle, F. (1954). 'On Nuclear Reactions Occurring in Very Hot Stars. I. the Synthesis of Elements from Carbon to Nickel'. The Astrophysical Journal Supplement Series. 1: 121. Bibcode:1954ApJS....1..121H. doi:10.1086/190005. ISSN0067-0049.
4. ^Chernykh, M.; Feldmeier, H.; Neff, T.; Von Neumann-Cosel, P.; Richter, A. (2007). 'Structure of the Hoyle State in C12'(PDF). Physical Review Letters. 98 (3): 032501. Bibcode:2007PhRvL..98c2501C. doi:10.1103/PhysRevLett.98.032501. PMID17358679.
5. ^Alshahrani, B.; Kibédi, T.; Stuchberry, A.E.; Williams, E.; Fares, S. (2013). 'Measurement of the radiative branching ratio for the Hoyle state using cascade gamma decays'. EPJ Web of Conferences. 63: 01022–1—01022–4. doi:10.1051/epjconf/20136301022.
6. ^Epelbaum, E.; Krebs, H.; Lee, D.; Meißner, U.-G. (2011). 'Ab Initio Calculation of the Hoyle State'(PDF). Physical Review Letters. 106 (19): 192501. arXiv:1101.2547. Bibcode:2011PhRvL.106s2501E. doi:10.1103/PhysRevLett.106.192501. PMID21668146.[permanent dead link]
7. ^Hjorth-Jensen, M. (2011). 'Viewpoint: The carbon challenge'. Physics. 4: 38. Bibcode:2011PhyOJ...4...38H. doi:10.1103/Physics.4.38.
8. ^News, Natalie Wolchover, Simons Science. 'The Hoyle State: A Primordial Nucleus behind the Elements of Life'. Scientific American. Retrieved 2020-12-06.
9. ^Kenji Takeshita and Masaru Ishidaa (December 2006). 'Optimum design of multi-stage isotope separation process by exergy analysis'. ECOS 2004 - 17th International Conference on Efficiency, Costs, Optimization, Simulation, and Environmental Impact of Energy on Process Systems. 31 (15): 3097–3107. doi:10.1016/j.energy.2006.04.002.

### Atomic Mass Number Of Carbon

 Lighter: carbon-11 Carbon-12 is an isotope of carbon Heavier: carbon-13 Decay product of: boron-12, nitrogen-12 Decay chain of carbon-12 Decays to: stable